My mom redirects the conversation whenever I begin to talk about obtaining a Power of Attorney. Any advice?

Sorry, I see I repeated part of what Veronica posted. 
Is your mom able to talk about other subjects? Stay on topic?
You may need to take her to an appointment with a certified elder law attorney and allow the attorney to speak to her and explain the necessity of taking action sooner rather than later.
Read the book ‘Being Mortal:Medication and what really matters” by Atul Gawande.

Mom clearly does not want to give up control. can you explain to her what will be likely to happen if she does not select someone to make decisions if she can't. Tell her she can decide ahead of time what she would want under certain circumstances. For example a very bad stroke. Would she want to be hooked up to a breathing machine, a feeding tube down her throat or any of the other things which can keep someone alive these days. Unless she has selected someone to make decisions the Drs will do everything possible to keep her alive. paint the worst possible picture.
Another alternative is to get her to an eldercare lawyer and let him or her explain it to Mom. As long as she is competent she cant be forced to do anything